Find the Decimal Between 0.66 and 0.67: Inequality Problem

Q: Why do I need to add zeros to the end of decimals?

Adding zeros helps you see all the place values clearly! When you write 0.66 as 0.660, you can easily compare it to 0.665 digit by digit from left to right.

Q: How do I know which decimal is between the two given numbers?

Look at each decimal place from left to right. The number between 0.660 and 0.670 must have the same first two digits (6 and 6) but a middle digit in the thousandths place.

Q: What if there are multiple correct answers?

You're right! There are many decimals between 0.66 and 0.67 (like 0.661, 0.662, 0.663...). Just pick the one that matches the given choices.

Q: Can 0.67 be the answer if the inequality uses < instead of ≤?

No! The symbol strictly smaller than 0.67.

Q: Is 0.656 between 0.66 and 0.67?

Let's check: 0.656 vs 0.660. Since 0.656 not between our range. Remember, we need a number greater than 0.66!

Decimal Ordering with Three-Digit Precision

What is the missing decimal number?

$0.66 < ? < 0.67$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the appropriate number

00:03 Let's use the number line to find the possible numbers

00:20 We can see that all these numbers fit

00:23 Let's choose the appropriate number from the options

00:26 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the missing decimal number?

$0.66 < ? < 0.67$

Step-by-step solution

In order to discover our range of numbers, we will first add 0 to both numbers as follows:

$0.66=0.660$

$0.67=0.670$

This means our number will be in the range between 0.660 and 0.670.

The numbers that exist in this range are: $0.661\text{ }0.662\text{ }0.663\text{ }0.664\text{ }0.665\text{ }0.666\text{ }0.667\text{ }0.668,\text{ }0.669$ .

Now if we look at the possible answers and compare them to our number range, we can deduce that the answer is 0.665 as it appears in both.

Final Answer

$0.665$

Key Points to Remember

Essential concepts to master this topic

Rule: Add zeros to match decimal places for comparison
Technique: Convert 0.66 to 0.660 and 0.67 to 0.670
Check: Verify 0.660 < 0.665 < 0.670 using place value ✓

Common Mistakes

Avoid these frequent errors

Comparing decimals without matching decimal places
Don't compare 0.66 and 0.665 directly = confusion about which is bigger! Without equal decimal places, students often think 0.665 is smaller than 0.66. Always add zeros to make equal decimal places before comparing.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why do I need to add zeros to the end of decimals?

Adding zeros helps you see all the place values clearly! When you write 0.66 as 0.660, you can easily compare it to 0.665 digit by digit from left to right.

How do I know which decimal is between the two given numbers?

Look at each decimal place from left to right. The number between 0.660 and 0.670 must have the same first two digits (6 and 6) but a middle digit in the thousandths place.

What if there are multiple correct answers?

You're right! There are many decimals between 0.66 and 0.67 (like 0.661, 0.662, 0.663...). Just pick the one that matches the given choices.

Can 0.67 be the answer if the inequality uses < instead of ≤?

No! The symbol < means 'less than' (not equal to). Since we need ? < 0.67, the answer cannot be 0.67 itself. It must be strictly smaller than 0.67.

Is 0.656 between 0.66 and 0.67?

Let's check: 0.656 vs 0.660. Since 0.656 < 0.660, it's not between our range. Remember, we need a number greater than 0.66!

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